Chapter 12 - Section 12.3 - Geometric Sequences - 12.3 Exercises - Page 865: 32

The common ratio is $\sqrt 2$. The fifth term is 4 $a _{n} = 1(\sqrt 2)^{n-1}$ (or just $a_{n} = (\sqrt 2)^{n-1}$)

We are given the terms 1 $\sqrt 2$, 2, $2\sqrt2$. Since each term is multiplied by $\sqrt2$ to get the next term the common ratio is $\sqrt 2$. The fifth term = the fourth term × $\sqrt 2$. (the common ratio). So the fifth term = $2\sqrt 2 \times \sqrt 2$ = 4. To write an equation for the nth term of the form $a_{n}=a(r)^{n−1}$ plug in the first term for a (1) and the common ratio for r ($\sqrt 2$) to get $a_{n} = (\sqrt 2)^{n-1}$